They absolutely can question intent. They just can’t use an “official act” as evidence of intent. They can use all the “unofficial acts” they want to demonstrate intent. And, once they decide that the bribe was an unofficial act, the door is opened to use it for intent as well.
The courts can’t even raise issue 2. That’s what you’re missing. Courts aren’t allowed to question the President’s intent.
How can you prove conspiracy if you can’t prove that all conspirators intended to commit a crime?
They absolutely can question intent. They just can’t use an “official act” as evidence of intent. They can use all the “unofficial acts” they want to demonstrate intent. And, once they decide that the bribe was an unofficial act, the door is opened to use it for intent as well.